Lies Boelen, Christophe Smet, Walter Van Assche
Published 2008-08-07Version 1
We present an asymmetric $q$-Painlev\'e equation. We will derive this using $q$-orthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this $q$-Painlev\'e equation (up to a simple transformation). We will show a stable method of computing a special solution which gives the recurrence coefficients. We establish a connection with $\alpha-q-P_V$.
Comments: 16 pages, 4 figures. Accepted, to appear in Journal of Difference Equations and Applications
Differential equations for the recurrence coefficients of semi-classical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach
Asymptotics of recurrence coefficients for the Laguerre weight with a singularity at the edge
Recurrence Coefficients of a New Generalization of the Meixner Polynomials
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